[tinypeach]

Hi Chemistry Forums,

I'm stuck on some energy calculations for different types of particles and waves. I've attached the questions and my answers. But I have no idea how to tackle the last question since I've only been given a temperature and no assigned wavelength. I assume there's an equation that includes temperature that I can apply here, but I'm not sure which.

Could anyone help me, please?

[Corribus]

Generally, the (average) translational kinetic energy of free particles, including neutrons, is

E = (3/2)k_BT

Where k_B is the Boltzmann constant. This is the same expression you would use for mono-atomic gas.

This is not the same as the most probably kinetic energy in the distribution.

This expression is for a collection of particles able to move in three mutually perpendicular directions. A question that I would have is whether a "beam" restricts the motion to one direction, in which case the number of degrees of freedom changes. Because I wasn't sure about this, I looked around for the kinetic energy of a neutron beam and there seem to be a few different answers, although some places refer to the mean, and some the mode of the distribution. So tbh I am not completely sure of the right way to treat this system.

Bottom line though is that the temperature relates to the kinetic energy through the Boltzmann distribution. The exact relation depends on how the motion is restricted and what statistical parameter you are interested in (mean, mode, median, etc.) since there will always be a distribution of energies.